This invention relates to a method for estimating the load-bearing capacity of a pile. It includes a method and apparatus for predicting the capacity or load bearing of a proposed or virtual pile, and a method and apparatus for measuring the estimated load bearing of an actual driven pile, including means for acquiring data from a pile being driven or an installed pile for the purposes of applying the present method to estimate its load bearing.
Of the few categories of foundation pile installation methods (such as driven, bored, injected, cast-in-place, caisson or floating, etc.) the method of this invention is based on the impact-driven or hammer-driven testing on an installed pile or pile under installation.
As the load bearing capacity of a pile is of the utmost importance in considering the design and installation of a building structure""s foundation, various methods have been employed to estimate the pile""s load bearing capacity. As the ultimate load bearing of a foundation is limited by either the structural strength of the pile or the capacity of the supporting soil (i.e. the xe2x80x9cpile-soilxe2x80x9d system), geotechnical engineers may, in most instances, choose or design the appropriate piles. The soil factor, on the other hand, are but predetermined by the proposed structure""s site and, hence, the soil profile can only be analysed and studied through soil tests.
The manner in which the adequacy of a pile chosen or designed in meeting the allowable loads is generally governed by building by-laws or standards such as the BS 8004:1986. The pile""s load bearing capacity may then be verified by one or more of the conventional tests such as static tests, dynamic tests or wave equation-based tests.
Static Test
Traditionally, the most relied upon pile testing has been the static load test which involves waiting for up to 30 days after pile driving to allow soil remoulding and settlement before stacking incrementally static weight loads onto the pile top and then measure the corresponding pile movements. In practice, static tests are performed to either (i) prove that it can safely hold the design load (proof test), or (ii) to determine a design load based on the ultimate load bearing capacity of the pile (i.e. load until failure).
Proof testing is more prevalent as the ultimate pile strength may often never be known. This results in higher capacity of the piles being laid and thus incurring greater foundation costs than are actually required. Moreover, due to the physical difficulty of stacking large weight blocks onto the pile top, the length of time and costs involved, only a small percentage of the piles on site are actually tested.
Dynamic Test
From the number of hammer blows in advancing a pile per unit of penetration, the energy from the hammer blows has been equated to the work done in advancing the pile against soil resistance, Based on Newton""s Second Law of Motion, i.e. the impulse-momentum principles, theoretical and semi-empirical formulae have been derived to express this relationship between energy and work by assuming the hammer and pile are rigid bodies and soil resistance as a constant static force. These formulas are generally known as Dynamic Formulae or Energy Formulae.
The model common to all the simple dynamic formulae may be illustrated in FIG. 1 where if potential energy stored in the ram is equated to the work done by advancing the pile against a constant soil resistance, then
Wh=Rs.
or                     R        =                              W            ⁢                          xe2x80x83                        ⁢            h                    s                                where                                    W          ⁢                      xe2x80x83                    ⁢          is          ⁢                      xe2x80x83                    ⁢          the          ⁢                      xe2x80x83                    ⁢          ram          ⁢                      xe2x80x83                    ⁢          weight                ;                                          R          ⁢                      xe2x80x83                    ⁢          is          ⁢                      xe2x80x83                    ⁢          the          ⁢                      xe2x80x83                    ⁢          soil          ⁢                      xe2x80x83                    ⁢          resistance          ⁢                      xe2x80x83                    ⁢          constant                ;                                          h          ⁢                      xe2x80x83                    ⁢          is          ⁢                      xe2x80x83                    ⁢          the          ⁢                      xe2x80x83                    ⁢          drop          ⁢                      xe2x80x83                    ⁢          height          ⁢                      xe2x80x83                    ⁢          of          ⁢                      xe2x80x83                    ⁢          the          ⁢                      xe2x80x83                    ⁢          ram                ;                                s        ⁢                  xe2x80x83                ⁢        is        ⁢                  xe2x80x83                ⁢        the        ⁢                  xe2x80x83                ⁢        pile        ⁢                  xe2x80x83                ⁢                  set          .                    
This basic dynamic pile capacity formula, which is also termed xe2x80x9crational pile formulaxe2x80x9d, and most of the other dynamic pile formulae currently in use are derived from this equation. [For examples, see Joseph E. Bowles, Foundation Analysis and Design, 4th edition, McGraw-Hill, 1988, p. 791].
The more common formulas derived from the above rational pile formula have incorporated various assumptions on certain parameters in order to improve on the reliability of predictions on the pile capacity; however, each formula gives a different value of the capacity of the same pile. Some are these formulas are given in the following Table 1 [from Bowles, p. 794].
Each of the formulas has its own advantages under different circumstances. For example, the Engineering News-Record (ENR) formula (1965) is thought to be reasonably valid over the entire range of load tests and has been cited as the most widespread dynamic formula in the U.S.A. It defines the soil resistance, R, in terms of the ultimate pile capacity, Pu, as the safe load in kips (1 kip=1000 lbs=453.6 kg) with xe2x80x9clossxe2x80x9d terms eh and Eh introduced and safety factor (SF) of 6 assigned. [Hussein, Likens and Rausche, Testing Methods of Driven Piles, Pile Buck, Inc., 1988].
The Hiley formula (1930) is found to have the least statistical deviation or the highest statistical correlation. In fact, the British Standard BS 8004:1986 cites the Hiley formula as one of the more reliable dynamic formulas and is probably the most commonly used in Britain.
Although dynamic formulas have been widely used to predict pile capacity, more accurate means is needed to determine when a pile has reached a satisfactory load-bearing value other than by simply driving it to some depth predetermined by the formulas. The pile driven to a predetermined depth may or may not obtain the required bearing value due to the complex pile and soil characteristics. Today, dynamic formulas are generally acknowledged as inaccurate due to their oversimplification of the modelling of the hammer, driving system, pile, and soil. In fact, they are not applicable to most hammer types used on today""s sites, long elastic piles, or cohesive, impermeable, compressible soils.
Wave Equation Analysis
Modern foundation engineering recognises that pile driving may be better estimated by wave propagation theories which may include complicated partial differential equations With the advent of digital computers in the 1950s it became possible to arrive at a discrete solution of wave propagation equations by algorithm using computer program codes, thus allowing for pile driving analysis.
Examples of such wave equation analysis programs widely used today are WEAP, WEAP86 and TTI which were developed under the U.S. Federal Highway Administration""s sponsorship in the 1960s. Further development and refinement lead to commercially available programs such as the following examples.
GRLWEAP(trademark) from Goble Rausche Likins and Associates, Inc. (GRL) and used often in analyses prior to actual pile installation. It has been claimed as the most widely used wave equation in predicting pile bearing capacity and driveability. It has also been used for analyses and selection of proper pile installation equipment prior to the installation of piles,
CAPWAP(trademark) (including its modifications such as CAPWAPC(trademark), etc.) or Case Pile Wave Analysis Program which was developed from the research conducted by Prof. G. G. Goble, F. Rausche and G. Likins which begun in 1964 at Case Institute of Technology, now Case Western Reserve University; hence also known as the Case Method. It is often used in analyses during and after pile installation in conjunction with a wide array of instrumentation system for field measurement from Pile Dynamics, Inc. (PDI); both the companies, GRL and PDI, based at Cleveland, Ohio, U.S.A., grew from Prof Goble""s the core research team;
TNOWAVE(trademark) from TNO Building and Construction Research, Delft, Netherlands;
SIMBAT(trademark) from Testconsult Ltd., Warrington, United Kingdom; etc.
Each of the above examplary methods uses slightly different modelling of the pile-soil model. However, probably due to the support and dissemination by the GRL and PDI groups of their method and field monitoring techniques, these two have become presently the leading pile analysis methods and apparatuses in the industry.
There are many other methods of stress wave transmission that may be used. A wide selection of suitable wave equation may be found at the Internet website entitled xe2x80x9cThe Wave Equation Page for Pilingxe2x80x9d at http://www.geocities.com/CapeCanaveral/Hangar/2955.
Convention wave equation-based analysis procedure consists of, firstly, assuming the soil resistance parameters and, secondly, perform the dynamic trial analysis. Then, the measured results is compared with the computed pile top parameters. If the match is not satisfactory, new soil resistance parameters are computed and the dynamic trial analysis is performed again. If the soil model output matches satisfactorily, it may then proceed to simulated static test. A computer program such as GRLWEAP, CAPWAP, TNOWAVE, etc. may be used to perform repetitive and tedious analysis and correlation calculations of the porcedure.
The execution of such a program may be made automatic by a computational tool integrated with on-line data acquisition means to obtain and the parameters for running the program. An example of such integrated apparatus is PDI""s Pile Driving Analyser(trademark) or PDA(trademark) which provides measurements taken on-line from a pile under driving hammer for the prediction method of static soil resistance.
Generally, the different parameters required for the execution of a wave equation analysis may be summarised in the following Table 2:
The final result is a simulated static load test, representing the pile-soil behaviour at the time of testing. Hence, a re-strike test should be performed sometime after pile installation. If records are also evaluated at the end of installation, then the change of soil strength can be evaluated as a function of time.
The present invention endeavours to provide an alternative method for analysing and estimating a pile""s load bearing capacity. Instead of using a wave equation, the present method employs the Impact Load Theory for both the simulated or virtual tests and actual field tests.
Basically, an xe2x80x9cimpact loadxe2x80x9d is a force delivered by a blow, as opposed to a force applied gradually and maintained over a long period. The Impact Load Theory is widely used in structural and mechanical engineering and may be found in any basic textbooks in such fields, for example in G. H. Ryder, Strength of Materials, 3rd ed, (1969), pages 9-12.
However, the Impact Load Theory is not known to have ever been applied in foundation or geotechnical engineering. Hence, the present invention proposes a new theoretical basis for estimating load bearing capacity of piles, i.e. by employing one or more equations derived from the Impact Load Theory.
The present invention provides for a method for estimating the load bearing capacity of a pile comprising obtaining the values of parameters including (i) the weight of an impact mass; (ii) the stroke height of the impact mass; (iii) the length of the pile; (iv) the cross sectional area of the pile; and (iv) the Young""s modulus of the pile; and calculate said capacity using one or more equation derived from Impact Load Theory.
In one embodiment of the invention, the equation derived from the Impact Load Theory is                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           P                                                  =                                                                                                      W                                                    ⁡                                                                                                          [                                                                                                              1                                                        +                                                                                                                                                                                                                                            1                                                              +                                                                                                                              2                                                                ⁢                                                                hAE                                                                                                                                                                                                                                                    WL                                                              e                                                                                                                                                                                                                                                                                          ]                                                                                                                                                                                                                                                                                                                                                                                          wherein                                                                                                                                                                                                                                                                                                                                                                                                                                    P                                              =                                                                                              the                                                ⁢                                                                                                  xe2x80x83                                                                                                ⁢                                                pile                                                ⁢                                                                                                  xe2x80x83                                                                                                ⁢                                                capacity                                                                                                                                      ;                                                                                                                                                                                                                                                                                                                                                                                                                  W                                        =                                                                                  the                                          ⁢                                                                                      xe2x80x83                                                                                    ⁢                                          weight                                          ⁢                                                                                      xe2x80x83                                                                                    ⁢                                          of                                          ⁢                                                                                      xe2x80x83                                                                                    ⁢                                          a                                          ⁢                                                                                      xe2x80x83                                                                                    ⁢                                          hammer                                                                                                                    ,                                                                              being                                        ⁢                                                                                  xe2x80x83                                                                                ⁢                                        the                                        ⁢                                                                                  xe2x80x83                                                                                ⁢                                        impact                                        ⁢                                                                                  xe2x80x83                                                                                ⁢                                        mass                                                                                                                                                                                                                                                                                                                                                                                      h                                  =                                                                      the                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    height                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    of                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    hammer                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    stroke                                                                                                  ;                                                                                                                                                                                                                                                                                                            L                              e                                                        =                                                          the                              ⁢                                                              xe2x80x83                                                            ⁢                              length                              ⁢                                                              xe2x80x83                                                            ⁢                              of                              ⁢                                                              xe2x80x83                                                            ⁢                              pile                                                                                ;                                                                                                                                                                                                            A                      =                                              the                        ⁢                                                  xe2x80x83                                                ⁢                        cross                        ⁢                                                  xe2x80x83                                                ⁢                        sectional                        ⁢                                                  xe2x80x83                                                ⁢                        area                        ⁢                                                  xe2x80x83                                                ⁢                        of                        ⁢                                                  xe2x80x83                                                ⁢                        pile                                                              ;                                                                                                                          E              =                              the                ⁢                                  xe2x80x83                                ⁢                                  Young                  '                                ⁢                s                ⁢                                  xe2x80x83                                ⁢                modulus                ⁢                                  xe2x80x83                                ⁢                of                ⁢                                  xe2x80x83                                ⁢                                  pile                  .                                                                                        Formula        ⁢                  xe2x80x83                ⁢        I            
In one specific embodiment of the invention, the equation derived from Formula I may be further derived and simplified to       Formula    ⁢          xe2x80x83        ⁢    II                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          R                                              =                                                                                                                                                                                                    2                                                    ⁢                                                    AEWh                                                                                                    L                                                                                                                                                                                                                                                                                                                                                          wherein                                                                                                                                                                                                                                                                                                                                                                                            R                                          =                                                                                      soil                                            ⁢                                                                                          -                                                                                        ⁢                                            resistance                                            ⁢                                                                                          xe2x80x83                                                                                        ⁢                                            load                                                                                                                          ⁢                                                                                  xe2x80x83                                                                                ,                                                                                  equivalent                                          ⁢                                                                                      xe2x80x83                                                                                    ⁢                                          to                                          ⁢                                                                                      xe2x80x83                                                                                    ⁢                                          P                                                                                ,                                                                                                                              load                                            ⁢                                                                                          xe2x80x83                                                                                        ⁢                                            bearing                                            ⁢                                                                                          xe2x80x83                                                                                        ⁢                                            of                                            ⁢                                                                                          xe2x80x83                                                                                        ⁢                                            pile                                                                                    ;                                                                                                                                                                                                                                                                                                                                                                                                              W                                    =                                                                          the                                      ⁢                                                                              xe2x80x83                                                                            ⁢                                      weight                                      ⁢                                                                              xe2x80x83                                                                            ⁢                                      of                                      ⁢                                                                              xe2x80x83                                                                            ⁢                                      hammer                                                                                                        ;                                                                                                                                                                                                                                                                                                    h                              =                                                              the                                ⁢                                                                  xe2x80x83                                                                ⁢                                height                                ⁢                                                                  xe2x80x83                                                                ⁢                                of                                ⁢                                                                  xe2x80x83                                                                ⁢                                hammer                                ⁢                                                                  xe2x80x83                                                                ⁢                                stroke                                                                                      ;                                                                                                                                                                                                                                  L                        =                                                  the                          ⁢                                                      xe2x80x83                                                    ⁢                          length                          ⁢                                                      xe2x80x83                                                    ⁢                          of                          ⁢                                                      xe2x80x83                                                    ⁢                          pile                                                                    ;                                                                                                                                                                A                  =                                      the                    ⁢                                          xe2x80x83                                        ⁢                    cross                    ⁢                                          xe2x80x83                                        ⁢                    sectional                    ⁢                                          xe2x80x83                                        ⁢                    area                    ⁢                                          xe2x80x83                                        ⁢                    of                    ⁢                                          xe2x80x83                                        ⁢                    pile                                                  ;                                                                                  E          =                      the            ⁢                          xe2x80x83                        ⁢                          Young              '                        ⁢            s            ⁢                          xe2x80x83                        ⁢            modulus            ⁢                          xe2x80x83                        ⁢            of            ⁢                          xe2x80x83                        ⁢                          pile              .                                          
In another embodiment of the invention, the method may be used in designing and/or selecting a pile for its load bearing capacity, and in pile-driving control.
In yet another embodiment of the method, the estimated load bearing results calculated from a pile under design and/or selection according to the method may be compared with a corresponding result calculated according to conventional dynamic formulae, or, alternatively, a corresponding result calculated according to a method based on wave propagation theory.
Still another embodiment is to compare the capacity calculated according to the present method based on a pile being driven or tested with the corresponding capacity calculated according to a wave equation-based method using measurements of actual displacement of the pile being driven or under test. Alternatively, it may be compared with the corresponding results obtained from a static test.
In one preferred embodiment of the method, soil coefficient parameters may be included in the equation to refine the accuracy of estimation. Preferably still, the parameters and results are stored to build up a database for on-demand analysis of pile capacity.
The present invention also provides for an apparatus for estimating the load bearing capacity of a pile comprising a computational tool which accepts the values of parameters including the weight of a hammer, the stroke height of the hammer, the length of the pile, the cross sectional area of the pile, and the Young""s modulus of the pile, and calculate said parameters according to an equation derived from the Impact Load theory.
In one preferred embodiment of the apparatus, the equation includes at least one of the above-stated Formulas I and II and the apparatus may be portable. In another preferred embodiment of the apparatus, the parameters are input online with data acquisition means from an actual pile under tests.